Solve {l}{4y+35=2}{9v+2w=7}{3v-8w=-2}

$$\left. \begin{array} { l } { 4 y + 35 = 2 } \\ { 9 v + 2 w = 7 } \\ { 3 v - 8 w = - 2 } \end{array} \right.$$

Solve for y, v, w

$$y = -\frac{33}{4} = -8\frac{1}{4} = -8.25$$

$$v=\frac{2}{3}\approx 0.666666667$$

$$w=\frac{1}{2}=0.5$$

Short Steps Using Substitution

Solve 4y+35=2 for y.

$$y=-\frac{33}{4}$$

Solve the second equation for v and the third equation for w.

$$v=-\frac{2}{9}w+\frac{7}{9} w=\frac{3}{8}v+\frac{1}{4}$$

Substitute -\frac{2}{9}w+\frac{7}{9} for v in the equation w=\frac{3}{8}v+\frac{1}{4}.

$$w=\frac{3}{8}\left(-\frac{2}{9}w+\frac{7}{9}\right)+\frac{1}{4}$$

Solve w=\frac{3}{8}\left(-\frac{2}{9}w+\frac{7}{9}\right)+\frac{1}{4} for w.

$$w=\frac{1}{2}$$

Substitute \frac{1}{2} for w in the equation v=-\frac{2}{9}w+\frac{7}{9}.

$$v=-\frac{2}{9}\times \frac{1}{2}+\frac{7}{9}$$

Calculate v from v=-\frac{2}{9}\times \frac{1}{2}+\frac{7}{9}.

$$v=\frac{2}{3}$$

The system is now solved.

$$y=-\frac{33}{4} v=\frac{2}{3} w=\frac{1}{2}$$